Algebraic versus geometric categorification of the~Alexander polynomial: a~spectral sequence

TL;DR

This paper introduces a spectral sequence connecting gl(0)-homology to knot Floer homology, utilizing advanced algebraic tools like quantum traces and singular bimodules to deepen understanding of knot invariants.

Contribution

It constructs a novel Bockstein-type spectral sequence linking algebraic and geometric knot invariants using sophisticated categorical and algebraic techniques.

Findings

Established a spectral sequence from gl(0)-homology to knot Floer homology.

Utilized quantum traces of foams and singular Soergel bimodules in the construction.

Provided new insights into the algebraic structures underlying knot invariants.

Abstract

We construct a bigraded spectral sequence from the gl(0)-homology to knot Floer homology. This spectral sequence is of Bockstein type and comes from a subtle manipulation of coefficients. The main tools are quantum traces of foams and of singular Soergel bimodules.